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ThinhN.
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Trên con đường thành côn...
18 tháng 10 2023 lúc 20:33

\(A=cos\left(7\pi-x\right)+3sin\left(\dfrac{3\pi}{2}+x\right)-cos\left(\dfrac{\pi}{2}-x\right)-sinx\)

\(=cos\left(x+\pi\right)+3sin\left(-\dfrac{\pi}{2}+x\right)-cos\left(\dfrac{\pi}{2}-x\right)-sinx\)

\(=-cosx-3cosx-sinx-sinx=-4cosx-2sinx\)

Bình Trần Thị
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Như Hồng Đặng
9 tháng 5 2016 lúc 12:26

a) P = cos(\(\frac{\Pi}{2}\) + x) + cos(2π - x) + cos(3π + x)   = -sinx + cosx - cosx = -sinx

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Lê Thị Thục Hiền
17 tháng 6 2021 lúc 20:48

\(A=cos\left(\dfrac{\pi}{3}+\alpha\right)+cos\left(\dfrac{\pi}{3}-\alpha\right)\)

\(=cos\dfrac{\pi}{3}.cos\alpha-sin\dfrac{\pi}{3}.sin\alpha+cos\dfrac{\pi}{3}.cos\alpha+sin\dfrac{\pi}{3}.sin\alpha\)

\(=2.cos\dfrac{\pi}{3}.cos\alpha=cos\alpha\)

Trần Ái Linh
17 tháng 6 2021 lúc 20:49

`A=cos(π/3 +α) + cos(π/3-α)`

`=cos π/3 . cos α - sin  π/3 . sinα + cos π/3 . cosα + sin π/3 . sinα`

`=2 . 1/2 . cos α`

`= cosα`

nguyen ngoc son
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Ngô Hằng
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Nguyễn Lê Phước Thịnh
25 tháng 6 2022 lúc 22:56

\(A=\cos\left(\text{π}-\dfrac{x}{2}\right)-\sin\left(\text{π}-x\right)\)

\(=\sin x+\sin x=2\cdot\sin x\)

\(B=\cos\left(2\text{π}+\dfrac{\text{π}}{2}-x\right)+\sin\left(4\text{π}+\dfrac{\text{π}}{2}-x\right)-\cos\left(6\text{π}+\dfrac{3}{2}\text{π}+x\right)-\sin\left(16\text{π}+\dfrac{3}{2}\text{π}+x\right)\)

\(=\sin x+\cos x-\cos\left(\dfrac{3}{2}\text{π}+x\right)-\sin\left(\dfrac{3}{2}\text{π}+x\right)\)

\(=\sin x+\cos x-\cos\left(\text{π}+\dfrac{\text{π}}{2}+x\right)-\sin\left(\text{π}+\dfrac{\text{π}}{2}+x\right)\)

\(=\cos x+\sin x+\cos\left(\dfrac{1}{2}\text{π}+x\right)+\sin\left(\dfrac{1}{2}\text{π}+x\right)\)

\(=\cos x+\sin x-\sin x+\cos x=2\cos x\)

Thiên Yết
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Lê Thị Thục Hiền
5 tháng 7 2021 lúc 6:39

\(A=sin\left(\dfrac{\pi}{2}-\alpha+2\pi\right)+cos\left(\pi+\alpha+12\pi\right)-3sin\left(\alpha-\pi-4\pi\right)\)

\(=sin\left(\dfrac{\pi}{2}-\alpha\right)+cos\left(\pi+\alpha\right)-3sin\left(\alpha-\pi\right)\)

\(=cos\alpha-cos\alpha+3sin\left(\pi-\alpha\right)\)\(=3sin\alpha\)

\(B=sin\left(x+\dfrac{\pi}{2}+42\pi\right)+cos\left(x+\pi+2016\pi\right)+sin^2\left(x+\pi+32\pi\right)+sin^2\left(x-\dfrac{\pi}{2}-2\pi\right)+cos\left(x-\dfrac{\pi}{2}+2\pi\right)\)

\(=sin\left(x+\dfrac{\pi}{2}\right)+cos\left(x+\pi\right)+sin^2\left(x+\pi\right)+sin^2\left(x-\dfrac{\pi}{2}\right)+cos\left(x-\dfrac{\pi}{2}\right)\)

\(=cosx-cosx+sin^2x+cos^2x+sinx\)

\(=1+sinx\)

\(C=sin\left(x+\dfrac{\pi}{2}+1008\pi\right)+2sin^2\left(\pi-x\right)+cos\left(x+\pi+2018\pi\right)+cos2x+sin\left(x+\dfrac{\pi}{2}+4\pi\right)\)

\(=sin\left(x+\dfrac{\pi}{2}\right)+2sin^2\left(\pi-x\right)+cos\left(x+\pi\right)+cos2x+sin\left(x+\dfrac{\pi}{2}\right)\)

\(=cosx+2sin^2x-cosx+1-2sin^2x+cosx\)

\(=1+cosx\)

Mai Anh
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Lê Thị Thục Hiền
18 tháng 5 2021 lúc 9:07

\(x+2y=\dfrac{\pi}{2}\)

\(\Leftrightarrow x+y=\dfrac{\pi}{2}-y\) thay vào A được:

\(A=\dfrac{cos\left(\dfrac{\pi}{2}-y\right)-cosy}{cos\left(\dfrac{\pi}{2}-y\right)+cosy}\)\(=\dfrac{siny-cosy}{siny+cosy}\)\(=\dfrac{\dfrac{\sqrt{2}}{2}.siny-\dfrac{\sqrt{2}}{2}.cosy}{\dfrac{\sqrt{2}}{2}.siny+\dfrac{\sqrt{2}}{2}cosy}\)\(=\dfrac{cos\dfrac{\pi}{4}.siny-sin\dfrac{\pi}{4}.cosy}{sin\dfrac{\pi}{4}.siny+cos\dfrac{\pi}{4}.cosy}\)

\(=\dfrac{sin\left(y-\dfrac{\pi}{4}\right)}{cos\left(y-\dfrac{\pi}{4}\right)}\)\(=tan\left(y-\dfrac{\pi}{4}\right)\)

Nguyễn Việt Lâm
18 tháng 5 2021 lúc 8:54

\(x+2y=\dfrac{\pi}{2}\Rightarrow x+y=\dfrac{\pi}{2}-y\)

\(\Rightarrow cos\left(x+y\right)=cos\left(\dfrac{\pi}{2}-y\right)\)

\(\Rightarrow cos\left(x+y\right)=siny\)

Do đó: \(A=\dfrac{siny-cosy}{siny+cosy}=\dfrac{\sqrt{2}sin\left(y-\dfrac{\pi}{4}\right)}{\sqrt{2}cos\left(y-\dfrac{\pi}{4}\right)}=tan\left(y-\dfrac{\pi}{4}\right)\)

Thảo Vi
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Nguyễn Việt Lâm
13 tháng 4 2021 lúc 23:55

1.

\(2cos\left(a+b\right)=cosa.cos\left(\pi+b\right)\)

\(\Leftrightarrow2cosa.cosb-2sina.sinb=-cosa.cosb\)

\(\Leftrightarrow2sina.sinb=3cosa.cosb\Rightarrow4sin^2a.sin^2b=9cos^2a.cos^2b\)

\(\Rightarrow4\left(1-cos^2a\right)\left(1-cos^2b\right)=9cos^2a.cos^2b\)

\(\Leftrightarrow4-4\left(cos^2a+cos^2b\right)=5cos^2a.cos^2b\)

\(A=\dfrac{1}{cos^2a+2\left(sin^2a+cos^2a\right)}+\dfrac{1}{cos^2b+2\left(sin^2b+cos^2b\right)}\)

\(=\dfrac{1}{2+cos^2a}+\dfrac{1}{2+cos^2b}=\dfrac{4+cos^2a+cos^2b}{4+2\left(cos^2a+cos^2b\right)+cos^2a.cos^2b}\)

\(=\dfrac{4+cos^2a+cos^2b}{4+2\left(cos^2a+cos^2b\right)+\dfrac{4}{5}-\dfrac{4}{5}\left(cos^2a+cos^2b\right)}=\dfrac{4+cos^2a+cos^2b}{\dfrac{24}{5}+\dfrac{6}{5}\left(cos^2a+cos^2b\right)}=\dfrac{5}{6}\)

Nguyễn Việt Lâm
13 tháng 4 2021 lúc 23:55

2.

\(A=2cos\dfrac{2x}{3}\left(cos\dfrac{2\pi}{3}+cos\dfrac{4x}{3}\right)=2cos\dfrac{2x}{3}\left(cos\dfrac{4x}{3}-\dfrac{1}{2}\right)\)

\(=2cos\dfrac{2x}{3}.cos\dfrac{4x}{3}-cos\dfrac{2x}{3}\)

\(=cos3x+cos\dfrac{2x}{3}-cos\dfrac{2x}{3}\)

\(=cos3x\)

\(B=\dfrac{cos2b-cos2a}{cos^2a.sin^2b}-tan^2a.cot^2b=\dfrac{1-2sin^2b-\left(1-2sin^2a\right)}{cos^2a.sin^2b}-tan^2a.cot^2b\)

\(=\dfrac{2sin^2a-2sin^2b}{cos^2a.sin^2b}-tan^2a.cot^2b=2tan^2a\left(1+cot^2b\right)-2\left(1+tan^2a\right)-tan^2a.cot^2b\)

\(=2tan^2a+2tan^2a.cot^2b-2-2tan^2a-tan^2a.cot^2b\)

\(=tan^2a.cot^2b-2\)

Nguyễn Việt Lâm
13 tháng 4 2021 lúc 23:59

3.

\(\dfrac{2sina}{cosa}=\dfrac{sin\left(a+b\right)}{cos\left(a+b\right)}\Leftrightarrow2sina.cos\left(a+b\right)=cosa.sin\left(a+b\right)\)

\(\Leftrightarrow sina.cos\left(a+b\right)=sin\left(a+b\right).cosa-cos\left(a+b\right)sina\)

\(\Leftrightarrow sina.cos\left(a+b\right)=sin\left(a+b-a\right)\)

\(\Leftrightarrow sina.cos\left(a+b\right)=sinb\)

b.

\(\dfrac{2sina}{cosa}=\dfrac{sin\left(a+b\right)}{cos\left(a+b\right)}\Leftrightarrow2sina.cos\left(a+b\right)=cosa.sin\left(a+b\right)\)

\(\Leftrightarrow sin\left(2a+b\right)+sin\left(-b\right)=\dfrac{1}{2}sin\left(2a+b\right)+\dfrac{1}{2}sinb\)

\(\Leftrightarrow\dfrac{1}{2}sin\left(2a+b\right)=\dfrac{3}{2}sinb\)

\(\Leftrightarrow sin\left(2a+b\right)=3sinb\)

Bap xoai
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Bap xoai
10 tháng 10 2023 lúc 19:52

Mn ơi cứu tui